Breaking the Bank

[Mark]

By looking at the patterns of the 5 and 7 always coming together and the 1,2 and 4's then I would guess that the combo is 2457?

[mike14]

it looks like any sequence of numbers will work as long as the next number is next to it and larger than the one before. 1 is next to 2, so it works, 2 is next to (diagnolly) 4. So, I believe that 1,2,3,4,5,6,7,8,9 would work beacuse all are next to eachother and each number next in the sequence is larger.

[Mark]

Yeah, and it would explain why the diagram of the numbers positions is given but then are all of the 57's a coincidence? Surely not.

[babw44]

Well, I could make perfect sense of it if it weren't for that 1,2 combination. All the others end in either 2 odd or 2 even numbers, and the last number is in the first column.

Also, none of the combinations have a number from the 3rd column in them. Why?

It is also true that in each combination, there are either more numbers from the 1st column than the second, or the same amount from each. Does this mean anything?

[cha]

Could we read the numbers as Braille dots? Then the letters given spell out C,O,N,F,I,R... Perhaps M is the next letter, 1,2,7?

[CrystyB]

That's too good an answer to NOT be the right one! Congratulations, cha!

[cjalmeida]

As the pressing order does not matter, we have the following combination:
We have 36 options on a two digits code: Combination 9 terms 2 slots: C(9,2)
We have 84 options on a three digits code: Combination 9 terms 3 slots: C(9,3)

...
We have 1 option on a nine digits code: Combination 9 terms 9 slots: C(9,9)

Which is:
C(9,2)+C(9,3)+C(9,4)+...+C(9,8)+C(9,9)=382 options.

minus 6, it gives us a chance of 1/376 to guess the right code!

It has given us three hints:
A) Pressing order does not matter.
B) The keypad MUST mean something.
C) The old codes MUST follow a pattern.

Now, let me think a little more about the puzzle and see if i can find a solution.

See ya!

[Sumudu2]

Braille dots! that's cool. good job seeing (hehe) that cha!

[Shadower]

I like the braille dots idea. It gave me an idea to see what the pattern of buttons would look like when the correct coe was entered and the buttons lit up. Based on that pattern I think the next combo is 1,4,5,7,8

[DropOfaHat]

I love Cha's suggestion, but! The problem is the puzzle specifically tells us that the order of the so-far-correct entries DOES NOT MATTER! So the fact that it spells most of a word (and "Confirm" at that!) shouldn't matter. It could just as well be MNIFCOR, in which case E doesn't necessarily make sense. I don't have a better suggestion yet, just thought I'd point that out...

[CrystyB]

I don't care. Puzzles have been known to have mistakes, and the solution (besides the fact that IT WORKS!) is too beautifull to be just a coincidence. 1,2,7 it must be.

On further thought, it isn't even a BIG mistake, it's a small confusion between the order of the combinations and the order within the combinations...

[Manu]

the Braille solution is the right one!!!
about the order:
there are 2 orders:
1) confirm, or mfricon
2) the order in which you press the 'dots' each time.

Since in the original question 'order' en 'press' are mentioned in the same sentence
-> Braille RULES

Manu

[hotep]

If the braille-system is correct and the next letter would be 'M' spelling out 'CONFIRM',
what should then be the next word to be spelled, or does it end there?

[Alter Ego]

If this helps anybody - I was there when this was initially posted and solved (in VSP) last year and CONFIRM or 1,2,7 (or any ordering to that effect) is indeed the final solution.

[DropOfaHat]

OK, I see, I misunderstood...

you guys of course are right, apparently it is the order within each combination that doesn't matter, which makes perfect sense - It would seem that the order of the group of combinations DOES matter, however.

I too wonder what happens next - can the lock ever be opened again??

[start pilot]

It must be an expensive lock when you have to replace it after 7 openings.

[CrystyB]

I have a lock that needs a certain combination. After i opened it, used whatever was locked, i would just close the lock and shuffle the digits around. I wouldn't need to change the lock, even though the combination is the same for ever and ever.

Or am i missing your point?

[DropOfaHat]

CrystyB, yes I think you're missing the point. The puzzle says that once a combination has been punched in, it will no longer work to open the lock. We're all a little bored now that the puzzle has been solved (very cleverly), so we're musing as to what happens after the 7th "letter" is punched in. Maybe it resets itslef? Or maybe the word is actually "CONFIRMATION", buying us 5 more openings...


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[jeep]

Of course CONFIRMATION would require that I be used twice...

-JEEP

[DropOfaHat]

Darned good point, Jeep

[mwf]

"COMFIRMATION" is not a valid answer. The puzzle said that code were at least 2 digit. The code for the letter "A" is 1. So it will not work with the puzzle. The words "CONFIRMED" or "COMFIRMLY" would fit inside the rules of the puzzle.

[Hotep]

What made us believe that the word we were looking for had to be an english word?
i.e In french the word 'confire' exist. Louis has been around in the world, why can it
not be that he is now currently 'working' in france. So, with everything we were told, can
we be absolutely sure the next combination would be 'M' (1,2,7) and not 'E' (1,5).

[start pilot]

Right, i wonder if my life depended on it, would i dare to type in the letter M ?
I admit, i don't see an alternative.

[This message has been edited by start pilot (edited 03-28-2002 12:08 PM).]

[BrevITy]

Hey guys - don't niggle over petty details - and come on over to Visitor Submitted Puzzles... I'm sure you'll find plenty more there to occupy you in a way more interesting manner...

[cha]

More ponderings...
There is no mention of any penalty for an incorrect guess, so the best strategy might be to simply try the letters that would seem to make the most sense - M then perhaps E... If that should fail, say if the letters were not intended to spell out any word, just go through the remaining letters of the alphabet until the lock opened (19 remaining letters when you eliminate A with only one dot). There might even be fewer tries necessary if you tried letters in order of higher number of dots to lower number of dots. What I'm trying to say is that if in the process of punching in a letter that takes 4 dots (like V - 1,4,7,8), you get the correct letter with only the first two dots(like B - 1,4), the door should then open. That's all...

[CrystyB]

LOVELY! Just lovely... Cha, please consider my advice: register, visit VSP a few times, wander around the GL a bit. I'm sure you'll find this plave VERY entertaining. And challenging too

[cha]

done.

[yttrium]

Okay, here's my guess and solution: First, map out the combinations of the keypad. A number indicates only position. Pressed indicates the switch is on, unpressed indicates it is off.

As a reminder, the positions are:

123
456
789

So for the combination 1,2, and indicating the sequence in binary:

110
000
000

shows that key 1 and key 2 are pressed.

The following are the given key combinations. There must be an association or a pattern with them from one to another, and I am presuming that sufficient information is in the problem to solve it. The sequence as stated in the problem is as follows:

110
000 For 1,2
000

100
010 For 1,5,7
100

110
010 For 1,2,5,7
100

110
100 For 1,2,4
000

010
100 For 2,4
000

100
110 For 1,4,5,7
100

Now for the pattern (that I can see): Place a fourth column to the right, and determine the parity of each row. The following sequence is generated down:


110 0
000 0 For 1,2
000 0

100 1
010 1 For 1,5,7
100 1

110 0
010 1 For 1,2,5,7
100 1

110 0
100 1 For 1,2,4
000 0

010 1
100 1 For 2,4
000 0

100 1
110 0 For 1,4,5,7
100 1

Read down, the combinations are: 000 111 011 010 110 101 In octal, they are 0,7,3,2,6,5 This would lead one to suppose that either a 4 (100) or a 1 (001) would be the next combination. The next combination will be the fewest required to press to achieve the appropriate parity of the row. For 4 (100), either combinations below would work:


Key result (on or off: Keys:

100 010 001 111 1, 2, or 3, or 1 and 2 and 3
000 110 011 101 None, 4 and 5, 5 and 6, 4 and 6
000 110 011 101 None, 7 and 8, 8 and 9, 7 and 9

For the minimum to work, it would be 1, 4, 5 (1 alone wouldn't work, the problem requires two keys be pressed at a minimum).

A similar outcome can be determined for the 001 sequence

000 110 101 011 No keys, 1 and 2, 1 and 3, 2 and 3
000 110 101 011 No keys, 4 and 5, 4 and 6, 5 and 6
100 010 001 111 7, 8, or 9, or all three keys

Because the 100 parity would use three keys that have the lowest sum, I'd go with that one. My guess would be therefore the 1,4,5 keys pressed would open the lock.

This scheme would also provide for a non-repeating sequence that still will open the combination. After 100, then 001, the parity sequence would repeat, you have to continue to use the fewest number of keys.

[The Cheshire Man]

Yttrium, did you not realize that the solution (and a rather elegant one it was, too) has already been posted earlier in the thread?

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Now you see me, now you don't... but keep smiling!

[yttrium]

Actually, yes. However, the answer does not fit the solution. To wit:

"However this combination lock is no ordinary lock. Every time a correct code is entered into it the buttons light up and the correct combination changes so you can never use that code again. "

Any solution that limits the combination to a possible set of 26 characters (the alphabet) does not meet the 'never use that code again' after 26 times. The scheme I presented does not have this limitation (it is potentially infinite, although you might have to press keys more than once. i.e. 1 = on, 1 (again) = off, 1(third time) = on. This does not seem to violate the 'doesn't matter in which order the keys are pressed' restriction).

Also, there are a total of nine pins on the keypad. Braille uses an array of only six dots (2X3). While it is true that the only known combinations use the 2x3 array subset of the 3x3 array keypad, the problem does not indicate that this must be true in all cases. For reference, the Braille alphabet is at http://www.braille.com/alph.html.

If the author (Neil Murrell) states that braille is the answer, then it is. I just don't think that it meets all of the restrictions of the problem.

[Pi&Mal]

Hello, we (Pi is my wife, I'm Mal) are new here so we don't want to disregard the obviously elegant solutions given so far.

However, as Yttrium said, we don't think the Braille solution meets all the requirements.

This is what we thought:

-only 5 digits were used in the previous codes, these are 1,2,4,5 and 7. Like a five digit numeration system. So possible numbers should be 12, 14, 15, 17, 21, 22, 24 [...] 121, 124, 125, 127 and so on...

-Digits are never repeated. This eliminates, 11, 22, 44, and 122, 111, 177 etc ...

-the order in that digits were pressed didn't matter, that for us means that 1-2 is exactly the same as 2-1 for the lock. This reduces dramatically the number of possibilities (not our problem, is lock maker's)
For three-digits-codes 124 is the same as 412, 421, 214, 241, 142...

-Let's suppose that codes with 3 digits are used once 2 digit codes were all used. Then the 4 digits combinations enter the scene. (that's not too ambitious for a guess)
Chances are (once eliminated the numbers as above): 1245, 1247, 1257, 1457, 2457

-We've been told that 1457 and 1257 were already used, this lead us to believe that 2457 (or any combination of those digits) is the answer. Or the next five-digits number which of course could only be 12457 (as indicated above it should work exactly the same as 75421, and you of course should throw the lock to the garbagge)

-Anyway, if the Braille solution is the right one, we would be very dissapointed since:

a- English is not our native language
b- We don't know Braille
c- Maths are universal

Bye and thank you for the patience !


Pi & Mal.

[cha]

Technically, this is a multiple choice puzzle. The puzzle asks us to select one of three responses: a) give it up, there's no way of knowing, b) ... the correct combo is..., or c) just punch anything and see what happens. A and C are effectively the same response. This leaves B, which implies it is possible to know the one correct response, and the Braille idea is the only one I've seen yet that can narrow the possiblities down to one. Also, having a limited use lock does not violate the conditions of the puzzle. Also, also, if you agree with me that A and C are for all practical purposes the same answer, one could solve this puzzle by answering "B" without having ever read the puzzle itself.

[i_h8_evil_stuff]

B

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The name explains it all.

[yttrium]

Hello Pi and Mal,

Looks like we're thinking along similar lines w.r.t. the order in which the digits are pressed. That's why I modeled the keypad in binary (on or off) switches--that way it doesn't matter. There are a couple of things to consider, though:

1. Digits are never repeated. Just because they aren't, does that mean that they won't? Also, just because a number (or key) is not used in the given sequence, does it follow that it will never be used? For example, in the sequence: 1,2,3,5 (prime numbers) you could deduce two things: first, that 4 will never be used, because it is not prime and second, that the next number in the sequence is 7, which is not actually a selection provided.

2. "-Let's suppose that codes with 3 digits are used once 2 digit codes were all used. Then the 4 digits combinations enter the scene. (that's not too ambitious for a guess)
Chances are (once eliminated the numbers as above): 1245, 1247, 1257, 1457, 2457"

The puzzle seems to indicate that the fifth sequence is a 2 digit code. Does that fit in with this?

There have been several excellent historical television shows on decryption efforts made of the German's Enigma and Japan's Purple machines during WWII. Enigma used a sequence of rotors that advanced on each keypress. I suspect that a similar scheme is the solution to this problem, but that it would be mathematically based (on prime factors, number of keypresses, AND/OR functions, etc) which would advance the next combination and allow for an infinite number of combinations.

Any thoughts?

[0z0ne]

As a fresh pair of eyes on this puzzle, I'm guessing that the next code based on pattern logic would be 4, 5.

[/dev/joe]

I like the Braille answer, but my answer is

c) Just punch anything in and see if any cool stuff happens.

There are only about 500 combinations; it'll open soon enough.

[groza528]

This puzzle reminds me of the original GL clocks puzzle in Paladincompetition1. I got that one immediately, I don't know why this one baffled me for so long.

[Gomez]

, that puzzle was my inspiration for this one.

[This message has been edited by Gomez (edited 04-11-2002 08:57 AM).]

[Mr. E]

This puzzle has many different solutions for the info givin. For instance I came up with graph coordinance, I added them up several different ways, and there are other ways I came up with.

[Gomez]

Well, the way I see it, any solution that works given the facts presented can't be called wrong, so well done